O'Grady's tenfolds from stable bundles on hyper-K\"ahler fourfolds

TL;DR

This paper constructs new hyper-K"ahler manifolds of type OG10 as moduli spaces of stable bundles on hyper-K"ahler fourfolds, and provides a modular approach to a compactification related to cubic fourfolds.

Contribution

It introduces a novel modular construction of OG10 hyper-K"ahler manifolds via stable bundles and links them to cubic fourfolds through a compactification.

Findings

Constructed infinitely many 20-dimensional families of OG10 hyper-K"ahler manifolds.

Provided a modular construction of the Laza--Saccà--Voisin compactification.

Connected hyper-K"ahler fourfolds with intermediate Jacobian fibrations.

Abstract

We provide a modular construction of the Laza--Sacc\`a--Voisin compactification of the intermediate Jacobian fibration of a cubic fourfold. Additionally, we construct infinitely many $20$-dimensional families of polarized hyper-K\"ahler manifolds of type OG10, realized as moduli spaces of stable bundles on hyper-K\"ahler manifolds of type $\mathrm{K3}^{[2]}$.